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- Exponential and Logarithmic functions

Still Confused?

Try reviewing these fundamentals first

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Try reviewing these fundamentals first

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Get Started Now- Lesson: 15:58
- Lesson: 27:05

We have previously learnt that applying logarithm on a humungous number will give us a much smaller number. Ever wondered how this property can help us in our daily lives? One of the many applications of logarithmic properties is to measure the magnitude of earthquakes, which we call the Richter magnitude scale. In this section, we will explore the concept of this logarithmic scale and its applications.

Basic Concepts: Exponents: Division rule ${a^x \over a^y}=a^{(x-y)}$

Related Concepts: Derivative of inverse trigonometric functions, Derivative of logarithmic functions

- 1.The 2011 earthquake in Japan measured 9.0 on the Richter scale.

The 2008 earthquake in China measured 7.9 on the Richter scale.

Complete the following 2 sentences:

(i) The Japan earthquake was __________ times as intense as the China

earthquake.

(ii) The China earthquake was __________ times as intense as the Japan

earthquake. - 2.Earthquake "Alpha" measured 5.8 on the Richter scale.

Earthquake "Beta" was 200 times as intense as Earthquake "Alpha".

Earthquake "Gamma" was ${ 1\over 1000 }$ times as intense as Earthquake "Alpha".

What was the Richter scale readings for:

(i) Earthquake "Beta"

(ii) Earthquake "Gamma".

6.

Exponential and Logarithmic functions

6.1

Converting from logarithmic form to exponential form

6.2

Evaluating logarithms without calculator

6.3

Common logarithms

6.4

Evaluating logarithms using change-of-base formula

6.5

Converting from exponential form to logarithmic form

6.6

Product rule of logarithms

6.7

Quotient rule of logarithms

6.8

Combining product rule and quotient rule in logarithms

6.9

Solving logarithmic equations

6.10

Evaluating logarithms using logarithm rules

6.11

Continuous growth and decay

6.12

Finance: Compound interest

6.13

Exponents: Product rule $(a^x)(a^y)=a^{(x+y)}$

6.14

Exponents: Division rule ${a^x \over a^y}=a^{(x-y)}$

6.15

Exponents: Power rule $(a^x)^y = a^{(x\cdot y)}$

6.16

Exponents: Negative exponents

6.17

Exponents: Zero exponent: $a^0 = 1$

6.18

Exponents: Rational exponents

6.19

Graphing exponential functions

6.20

Graphing transformations of exponential functions

6.21

Finding an exponential function given its graph

6.22

Logarithmic scale: Richter scale (earthquake)

6.23

Logarithmic scale: pH scale

6.24

Logarithmic scale: dB scale

6.25

Finance: Future value and present value

We have over 830 practice questions in Precalculus for you to master.

Get Started Now6.1

Converting from logarithmic form to exponential form

6.2

Evaluating logarithms without calculator

6.3

Common logarithms

6.4

Evaluating logarithms using change-of-base formula

6.5

Converting from exponential form to logarithmic form

6.6

Product rule of logarithms

6.11

Continuous growth and decay

6.12

Finance: Compound interest

6.13

Exponents: Product rule $(a^x)(a^y)=a^{(x+y)}$

6.14

Exponents: Division rule ${a^x \over a^y}=a^{(x-y)}$

6.15

Exponents: Power rule $(a^x)^y = a^{(x\cdot y)}$

6.16

Exponents: Negative exponents

6.18

Exponents: Rational exponents

6.22

Logarithmic scale: Richter scale (earthquake)

6.23

Logarithmic scale: pH scale

6.24

Logarithmic scale: dB scale

6.25

Finance: Future value and present value